B. Matter, Chemical Trends, and Chemical Bonding · Matter, Chemical Trends, and Chemical BondingElectron Arrangement, the Periodic Law and Effective Nuclear Charge
B3.3 B2.1 A2.2About 65 minutes
Learning goals- I can state the periodic law and explain how Mendeleev and Moseley contributed to it.
- I can use the periodic table to give the electron arrangement and valence electrons of the first 20 elements.
- I can estimate the effective nuclear charge felt by valence electrons.
- I can use charge and distance to explain how tightly an atom holds its valence electrons.
Words to know
periodic law
When elements are arranged by increasing atomic number, their properties repeat at regular intervals.
valence electrons
Electrons in the outermost occupied shell of an atom.
core electrons
Electrons in the inner shells of an atom, between the nucleus and the valence shell.
shielding
The reduction of the nucleus's pull on valence electrons caused by the core electrons between them.
effective nuclear charge (Zeff)
The net positive charge felt by a valence electron; roughly Z minus the number of core electrons.
period / group
A horizontal row / a vertical column of the periodic table.
A table that made predictions
In 1869 the Russian chemist Dmitri Mendeleev arranged the 63 elements known at the time in order of atomic mass and grouped elements with similar properties. Where the pattern did not fit, he left gaps and predicted that new elements would be found to fill them. One gap sat below silicon. Mendeleev predicted its atomic mass, density and the formula of its oxide. In 1886 germanium was discovered, and its properties matched his predictions closely.
A good scientific model does not just describe; it predicts. In this lesson you will see what the periodic table is really built on, and meet a new idea, effective nuclear charge, that explains almost every trend in this unit.
Remember from Grade 9
You learned that elements in the same group (column) have the same number of valence electrons and similar chemical properties, and that the period (row) number tells you how many electron shells an atom has. You drew Bohr-Rutherford diagrams with 2 electrons in the first shell and up to 8 in the next shells for the first 20 elements.
The periodic law
Mendeleev ordered elements by atomic mass. A few pairs ended up in the wrong place: tellurium (127.6 u) is heavier than iodine (126.9 u), but iodine clearly belongs with the halogens. In 1913 the English physicist Henry Moseley used X-rays to measure the positive charge of each nucleus and showed that the real ordering number is the atomic number. That fixed the problem. Today's statement is the periodic law:
When the elements are arranged in order of increasing atomic number, their properties repeat at regular intervals (periodically).
Why do properties repeat? Because electron arrangements repeat. Every time a new shell starts, the number of valence electrons goes back to 1.
Electron arrangement and the table
For the first 20 elements, electrons fill shells in this order: up to 2 in shell 1, up to 8 in shell 2, up to 8 in shell 3, then shell 4 starts with potassium and calcium.
- Period number = number of occupied shells. Sulfur is in period 3, so its electrons are in 3 shells: 2, 8, 6.
- Valence electrons (electrons in the outer shell): groups 1 and 2 have 1 and 2; groups 13 to 18 have 3 to 8 (subtract 10 from the group number). Helium is the exception: 2.
- Elements with the same number of valence electrons react in similar ways, because chemical reactions involve the outer electrons.
From the transition metals on, electron arrangements are more complicated. You will learn the full quantum-mechanical model, with orbitals, in Grade 12 Chemistry (SCH4U).
Effective nuclear charge
A valence electron is pulled towards the positive nucleus. But it is also pushed away by the other electrons, especially the inner (core) electrons that sit between it and the nucleus. The core electrons shield the valence electron from part of the nuclear charge.
The effective nuclear charge (Zeff) is the net positive charge a valence electron actually "feels". A simple estimate is:
Zeff ≈ Z − (number of core electrons)
- Sodium: Z = 11, core electrons = 10 (2 + 8), so Zeff ≈ +1.
- Chlorine: Z = 17, core electrons = 10, so Zeff ≈ +7.
Notice that for main-group elements this simple estimate is the same as the number of valence electrons. (More exact calculations give values that are not whole numbers, because valence electrons also shield each other a little and spend some time close to the nucleus. The simple model gives the right trends, which is what we need.)
Two rules that explain the trends
The pull of the nucleus on a valence electron depends on two things, just like the force between any two charges:
- Charge: a larger Zeff pulls harder.
- Distance: an electron in a shell farther from the nucleus is pulled less.
Across a period (left to right): electrons are added to the same shell, and protons are added to the nucleus, but the number of core electrons does not change. So Zeff increases and valence electrons are held more tightly and closer to the nucleus.
Down a group: Zeff stays about the same (it is +1 for all of group 1 in the simple model), but each period adds a new shell. The valence electrons are farther away and there are more core electrons in between, so they are held less tightly.
Keep these two sentences in mind. In the next three lessons you will use them to explain atomic size, ionization energy, electron affinity and electronegativity.
Worked exampleExample 1: Electron arrangement from the table
Without drawing, give the number of shells, the electron arrangement and the number of valence electrons for (a) phosphorus, (b) calcium, (c) argon.
- (a) Phosphorus, Z = 15, is in period 3 and group 15. Three shells: 2, 8, 5. Valence electrons: 15 − 10 = 5.
- (b) Calcium, Z = 20, is in period 4 and group 2. Four shells: 2, 8, 8, 2. Valence electrons: 2.
- (c) Argon, Z = 18, is in period 3 and group 18. Three shells: 2, 8, 8. Valence electrons: 8 (a full outer shell, which is why argon is so unreactive).
Period gives the number of shells, group gives the valence electrons, and the total must equal Z.
Worked exampleExample 2: Estimating effective nuclear charge
Estimate Zeff for the valence electrons of (a) magnesium and (b) sulfur. Which element holds its valence electrons more tightly? Explain.
- Magnesium: Z = 12, arrangement 2, 8, 2. Core electrons = 10. Zeff ≈ 12 − 10 = +2.
- Sulfur: Z = 16, arrangement 2, 8, 6. Core electrons = 10. Zeff ≈ 16 − 10 = +6.
- Both have valence electrons in shell 3 (same distance level), so the one with the larger Zeff pulls harder.
Sulfur holds its valence electrons more tightly, because it has a larger effective nuclear charge (+6 vs +2) at about the same distance.
Worked exampleExample 3: Down a group
Fluorine (2, 7) and chlorine (2, 8, 7) are both halogens. Compare Zeff and distance for their valence electrons, and predict which holds them more tightly.
- Fluorine: Z = 9, core = 2, so Zeff ≈ +7.
- Chlorine: Z = 17, core = 10, so Zeff ≈ +7.
- Same Zeff, but chlorine's valence electrons are in shell 3, farther away than fluorine's (shell 2).
Fluorine holds its valence electrons more tightly, because they are closer to the nucleus.
Just for funI'd tell you a chemistry joke about sodium, but Na.
| Atomic mass (u) | Formula of chloride (X = the element) |
|---|
| 14.01 | XCl₃ |
| 30.97 | XCl₃ |
| 28.09 | XCl₄ |
| 35.45 | XCl |
| 32.06 | XCl₂ |
| 12.01 | XCl₄ |
| 19.00 | XCl |
| 6.94 | XCl |
| 9.01 | XCl₂ |
| 40.08 | XCl₂ |
| 39.10 | XCl |
| 16.00 | XCl₂ |
| 10.81 | XCl₃ |
| 24.31 | XCl₂ |
| 26.98 | XCl₃ |
| 22.99 | XCl |
Hands-on activityBe Mendeleev for an evening
You need: 16 index cards (or scraps of paper) and a pencil.
Copy one row of the table above onto each card, without the element's name, just the atomic mass and the formula of the compound it forms with chlorine. Shuffle the cards.
- Put the cards in order of increasing atomic mass.
- Start a new row each time the chloride formula pattern starts over (XCl, XCl₂, XCl₃...). You should end up with rows that line up in columns.
- Now check your arrangement against a periodic table and write the real symbol on each card.
- Which columns have the same formula? How does the number of Cl atoms relate to the number of valence electrons?
What to look for: rows of Li to F, Na to Cl, then K and Ca. The number of Cl atoms rises 1, 2, 3, 4 for groups 1, 2, 13 and 14, then falls 3, 2, 1 for groups 15, 16 and 17. (The noble gases are left out because they do not form chlorides easily.)
Your turn
When elements are arranged in order of increasing atomic number, their properties repeat periodically.
2Give the electron arrangement of (a) aluminium, (b) potassium.
(a) Al, Z = 13: 2, 8, 3. (b) K, Z = 19: 2, 8, 8, 1.
3How many valence electrons does an element in group 16 have? Name one such element.
6. Examples: oxygen or sulfur.
4Estimate Zeff for a valence electron in (a) nitrogen and (b) silicon.
(a) N: 7 − 2 = +5. (b) Si: 14 − 10 = +4.
5Why do elements in the same group have similar chemical properties?
They have the same number of valence electrons, and chemical reactions involve the valence electrons.
6Explain, using Zeff, why valence electrons are held more tightly as you go across period 2.
Each step adds a proton but no new core electrons, so Zeff increases while the electrons stay in the same shell. The stronger pull holds them more tightly.
More practice: warm-up
1What does the period number tell you about an atom?
The number of occupied electron shells.
2Who first arranged elements by atomic number, using X-ray evidence?
3How many valence electrons does magnesium have?
The electrons in the inner shells, between the nucleus and the valence shell.
5Which has more shells, oxygen or sulfur?
Sulfur (3 shells; oxygen has 2).
More practice: on your own
1Mendeleev put tellurium (127.6 u) before iodine (126.9 u) even though this broke his atomic-mass order. Explain why he did this and how Moseley's work showed he was right.
Iodine's properties match the halogens (Cl, Br), so it belongs in group 17, after tellurium. Moseley showed that the true order is atomic number: Te is 52 and I is 53, so Te really does come first.
2Compare the valence electrons of sodium and potassium: Zeff, shell, and which is held more tightly.
Both Zeff ≈ +1. Sodium's valence electron is in shell 3; potassium's is in shell 4, farther away. Sodium holds its valence electron more tightly.
3An element has the arrangement 2, 8, 4. Identify it and give its group and period.
Z = 14: silicon, group 14, period 3.
4Why is helium placed above neon in group 18 even though it has only 2 valence electrons?
Helium's shell is full with 2 electrons, so like neon (full shell of 8) it is very unreactive. Its properties match the noble gases.
5Estimate Zeff for oxygen and for sulfur. Which holds its valence electrons more tightly, and why?
Both ≈ +6 (O: 8 − 2; S: 16 − 10). Oxygen's valence electrons are in shell 2, closer to the nucleus, so oxygen holds them more tightly.
Challenge
1Mendeleev predicted "eka-aluminium", the missing element below aluminium. It was discovered in 1875 and named gallium. Use the periodic law to predict the formula of gallium's chloride and its oxide. (Aluminium forms AlCl₃ and Al₂O₃.)
Gallium is in the same group as aluminium, so it should have 3 valence electrons and form GaCl₃ and Ga₂O₃, which is correct.
2The simple model says Zeff for all of group 1 is +1. Yet experiments show the outer electron of caesium is removed much more easily than that of lithium. Use the two rules from this lesson to explain why.
With equal Zeff, the deciding factor is distance. Caesium's valence electron is in shell 6, far from the nucleus, with many layers of core electrons in between, so the attraction is much weaker than for lithium's electron in shell 2.
3A student says, "Chlorine has 17 protons and potassium has 19, so potassium must hold its valence electron more tightly." Explain the error using effective nuclear charge.
Total protons is not what matters; shielding cancels most of them. Chlorine: Zeff ≈ 17 − 10 = +7 in shell 3. Potassium: Zeff ≈ 19 − 18 = +1 in shell 4. Chlorine's valence electrons feel a much larger net charge at a smaller distance, so chlorine holds them more tightly.
Quiz
1. The modern periodic law says that properties of elements repeat when they are arranged by increasing
2. What is the electron arrangement of chlorine?
3. Using Zeff ≈ Z − core electrons, the valence electrons of phosphorus feel a charge of about
4. Going across a period from left to right, effective nuclear charge
5. Why does potassium hold its valence electron less tightly than sodium?
6. Mendeleev's table was convincing mainly because it
Big idea: This lesson gives the reason behind the periodic table (expectation B3.3: the periodic law and trends explained by electron arrangement) and introduces effective nuclear charge, one of the terms in expectation B2.1. Every trend in the next lessons comes back to two rules: more net charge pulls harder; more distance pulls less.
How to help: Have your teen explain the two rules to you in their own words with an analogy (for example, a magnet pulls a paper clip more strongly if the magnet is stronger, and less strongly if there are many sheets of paper in between). The card-sort activity is a good shared puzzle.
Common difficulties:
- Thinking more protons always means a stronger pull. Core electrons cancel most of the extra charge down a group.
- Mixing up groups (columns) and periods (rows).
- Forgetting that helium has 2 valence electrons, not 8.